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Correlation and the time interval over which the variables are measured – A non-parametric approach

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  • Edna Schechtman
  • Amit Shelef

Abstract

It is known that when one (or both) variable is multiplicative, the choice of differencing intervals (n) (for example, differencing interval of n = 7 means a weekly datum which is the product of seven daily data) affects the Pearson correlation coefficient (ρ) between variables (often asset returns) and that ρ converges to zero as n increases. This fact can cause the resulting correlation to be arbitrary, hence unreliable. We suggest using Spearman correlation (r) and prove that as n increases Spearman correlation tends to a limit which only depends on Pearson correlation based on the original data (i.e., the value for a single period). In addition, we show, via simulation, that the relative variability (CV) of the estimator of ρ increases with n and that r does not share this disadvantage. Therefore, we suggest using Spearman when one (or both) variable is multiplicative.

Suggested Citation

  • Edna Schechtman & Amit Shelef, 2018. "Correlation and the time interval over which the variables are measured – A non-parametric approach," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-9, November.
    • Handle: RePEc:plo:pone00:0206929
    DOI: 10.1371/journal.pone.0206929
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    4. Jea, Rong & Lin, Jin-Lung & Su, Chao-Ton, 2005. "Correlation and the time interval in multiple regression models," European Journal of Operational Research, Elsevier, vol. 162(2), pages 433-441, April.
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